"You are disoriented. Blackness swims toward you like a school of eels who have just seen something that eels like a lot." ~ Douglas Adams

Symmetry and the Fourth Dimension (Part 2)

The Coxeter group of the cube

Coxeter groups are a huge amount of fun. Normally their delights are reserved for people who have already studied group theory. But I don’t think that’s fair. You don’t need to know music theory to enjoy a piece by Bach. And you don’t need to know group theory to enjoy Coxeter groups.

In fact, it’s probably better to learn theories after falling in love with some examples. Imagine a world where you had to learn music theory before listening to music. A world where everyone studied music theory in elementary school, high school and college, but only people who majored in music were allowed to listen to the stuff. In that world, people might say they hate music… just as in this world they say they hate math.

"A good stock of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one." - Paul Halmos